The diagonals of a rectangle ABCD meet at O. If angle BOC is equal to 44 degree, find angle OAD.
180-44=136 degrees
The diagonals of a rectangle produce pairs of isosceles triangle.
So triangle BOC is isosceles, and each of the base angles must be 68°
(68+68+44=180)
since angles BCO and OAD are alternate angles for parallel lines,
angle OAD = 68°
In a rectangle, the diagonals are equal in length and bisect each other. This means that ∠BOC and ∠AOD are congruent.
Given that ∠BOC is 44 degrees, we can conclude that ∠AOD is also 44 degrees. Therefore, angle OAD is 44 degrees.
To find angle OAD, we need to use the fact that the opposite angles of a rectangle are equal.
Let's start by drawing a rectangle ABCD and its diagonals, as shown:
A_______B
| |
| |
|__O___|
| |
D_______C
Given that angle BOC is equal to 44 degrees, we can say that angle AOD (which is opposite to angle BOC) is also equal to 44 degrees.
Now, since the opposite angles of a rectangle are equal, angle AOD is equal to angle AOB. We can consider triangle AOB and triangle AOD in order to find angle OAD.
In triangle AOB, the sum of angles is 180 degrees. We know that angle AOB is equal to 44 degrees, and angle OAB (which is equal to angle OAD) - let's call it x - is what we're trying to find.
So, we have: x + 44 + 90 = 180 (since angle OAB + angle AOB + angle ABO = 180)
Simplifying, we get: x + 134 = 180
Subtracting 134 from both sides, we get: x = 46
Therefore, angle OAD is equal to 46 degrees.